The coupling constants, \(g_{\sigma N}\) , \(g_{\omega N}\) , and the meson mean-fields, \(\langle \sigma \rangle _0\) , \(\langle \omega _0\rangle _0\)  are determined so as to reproduce the properties of the SNM with saturation density \(\rho _0\)  and the binding energy \(B_0\)  (=16.3 MeV), together with the equations of motion for the \(\sigma \)  and \(\omega \)  mean-fields, \(m_\sigma ^2\langle \sigma \rangle _0=g_{\sigma N}\rho _N^s\)  with the nuclear scalar density \(\rho _N^s\) , and \(m_\omega ^2\langle \omega _0\rangle _0=g_{\omega N}\rho _0\) . Further, the coupling constant \(g_{\rho N}\)  and the parameters \(\gamma _a\) , \(\eta _a\)  in TNA associated with isospin-dependence are obtained to meet empirical values of the incompressibility \(K\) =240 MeV [1]}, the symmetry energy \(S_0\)  (=31.5 MeV) [2]} for a given value of the slope \(L\) , which is defined as
\(L\)\(\equiv 3\rho _0\left(\partial S / \partial \rho _B\right)_{\rho _B=\rho _0, x=1/2}=3 P_{\rm neutron \ matter}(\rho _0) / \rho _0 \) . There is controversy about the empirical value of \(L\) , ranging from 30 MeV to 90 MeV [3]}, [4]}, [5]}. On the other hand, there are rather larger values estimated from the observations associated with \(X\) -ray bursters [6]}. Recent PREX-II experiments on measurement of the neutron skin thickness of \(^{208}\) Pb have also reported a large value of \(L\)  = (73\(-\) 146) MeV [7]}.
We take the lower values \(L\)  = (60\(-\) 70) MeV so that the density-dependence of the energy contributions around \(\rho _0\)  in SNM does not deviate much from those obtained by the standard variational calculation in terms of the \(V_{14}\)  two-body potential with addition of the phenomenological TNI by Lagaris-Pandahripande [LP (1981)] [8]} [e.g., see Fig. REF  for \(L\)  = 65 MeV].
In Table REF , the relevant quantities with the MRMF+UTBR+TNA model are listed for typical cases of \(L\)  = (60, 65, 70) MeV.
